An investigation of the efficacy of the Office of the Auditor-General in ensuring public financial accountability in the Gauteng Province
- Authors: Khumalo, Mildred Tariro
- Date: 2007
- Subjects: Finance, Public -- South Africa , Budget -- South Africa -- Gauteng , Liability (Law)
- Language: English
- Type: Thesis , Masters , MPA
- Identifier: vital:11645 , http://hdl.handle.net/10353/283 , Finance, Public -- South Africa , Budget -- South Africa -- Gauteng , Liability (Law)
- Description: Increasing accountability is a key element in a wide variety of governance reforms, from national level, public sector restructuring, to anti corruption campaigns and to centralise service delivery at local levels. (Van Wyk, 2002:311). Financial accountability has a major effect on performance issues, and these two combined have implications on democratic accountability. It is obviously a fact that when public officials become accountable, this will have a positive effect on service delivery. The introduction of the Public Finance Management Act (PFMA) 1999 (Act 1 of 1999) as amended by Act 29 of 1999 adopts an approach to financial management, which emphasises the need for accountability of results by focusing on output and responsibility rather than the rule driven approach of the previous Exchequer Acts. One quickly realises that the PFMA aims to regulate financial management at both National and Provincial levels of government. It directs attention at revenue, expenditure, assets and liabilities and aims to see that these are managed efficiently and effectively. Public finance accountability is increasingly becoming important in the public sector. One means of effecting accountability is through auditing. For this reason the Office of the Auditor -General through the Constitution of the Republic of South Africa 1996 (Act 108 of 1996 section 216 (1)) was established to facilitate effective accountability through auditing. The Office of the Auditor -General’s role is by no means minor, for it plays a major role in curbing corruption and acts as a ‘watchdog’ of the nation over public funds. Amidst high mismanagement and misuse of public resources, as well as corruption, especially in developing countries, the major question one asks is how effective the Auditor -General can be in ensuring effective public financial management and accountability within state departments so as to improve service delivery.
- Full Text:
- Authors: Khumalo, Mildred Tariro
- Date: 2007
- Subjects: Finance, Public -- South Africa , Budget -- South Africa -- Gauteng , Liability (Law)
- Language: English
- Type: Thesis , Masters , MPA
- Identifier: vital:11645 , http://hdl.handle.net/10353/283 , Finance, Public -- South Africa , Budget -- South Africa -- Gauteng , Liability (Law)
- Description: Increasing accountability is a key element in a wide variety of governance reforms, from national level, public sector restructuring, to anti corruption campaigns and to centralise service delivery at local levels. (Van Wyk, 2002:311). Financial accountability has a major effect on performance issues, and these two combined have implications on democratic accountability. It is obviously a fact that when public officials become accountable, this will have a positive effect on service delivery. The introduction of the Public Finance Management Act (PFMA) 1999 (Act 1 of 1999) as amended by Act 29 of 1999 adopts an approach to financial management, which emphasises the need for accountability of results by focusing on output and responsibility rather than the rule driven approach of the previous Exchequer Acts. One quickly realises that the PFMA aims to regulate financial management at both National and Provincial levels of government. It directs attention at revenue, expenditure, assets and liabilities and aims to see that these are managed efficiently and effectively. Public finance accountability is increasingly becoming important in the public sector. One means of effecting accountability is through auditing. For this reason the Office of the Auditor -General through the Constitution of the Republic of South Africa 1996 (Act 108 of 1996 section 216 (1)) was established to facilitate effective accountability through auditing. The Office of the Auditor -General’s role is by no means minor, for it plays a major role in curbing corruption and acts as a ‘watchdog’ of the nation over public funds. Amidst high mismanagement and misuse of public resources, as well as corruption, especially in developing countries, the major question one asks is how effective the Auditor -General can be in ensuring effective public financial management and accountability within state departments so as to improve service delivery.
- Full Text:
Assessment of antibacterial potentials of Garcinia Kola seed extracts and their interactions with antibiotics
- Authors: Sibanda, Thulani
- Date: 2007
- Subjects: Drug resistance in microorganisms , Garcinia , Antibiotics , Medicinal plants
- Language: English
- Type: Thesis , Masters , MSc (Microbiology)
- Identifier: vital:11242 , http://hdl.handle.net/10353/71 , Drug resistance in microorganisms , Garcinia , Antibiotics , Medicinal plants
- Description: The antibacterial potency of the extracts of the seed of Garcinia kola (bitter kola) was investigated in this study against a panel of referenced, environmental and clinical bacterial strains. The killing rates of the active extract as well as their potential for combination antibacterial therapy with standard antibiotics were also elucidated using standard procedures. The aqueous and acetone extracts of the seed were screened for activity against 27 bacterial isolates. The aqueous extract exhibited activity mainly against Gram positive organisms with Minimum inhibitory concentration (MIC) values ranging from 5 mgml-1 – 20 mgml-1, while the acetone extract showed activity against both Gram negative and Gram positive organisms with MIC values ranging from 10 mgml-1 - 0.156 mgml-1. The acetone extract also showed rapid bactericidal activity against Staphylococcus aureus ATCC 6538 with a 3.097 Log10 reduction in counts within 4 hours at 0.3125 mgml-1 and a 1.582 Log10 reduction against Proteus vulgaris CSIR 0030 at 5 mgml-1 after 1 hour. In addition, the aqueous, methanol and acetone extracts of the seeds also exhibited activity against four clinical strains of Staphylococcus isolated from wound sepsis specimens. The MIC values for the aqueous extract were 10 mgml-1 for all the isolates while the acetone and methanol extracts had lower values ranging from 0.3125 - 0.625 mgml-1. The acetone extract was strongly bactericidal against Staphylococcus aureus OKOH3 resulting in a 2.70 Log10 reduction in counts at 1.25 mgml-1 within 4 hours of exposure and a complete elimination of the organism after 8 hours. The bactericidal vi activity of the same extract against Staphylococcus aureus OKOH1 was weak, achieving only a 2.92 Log10 reduction in counts at 1.25 mgml-1 (4× MIC) in 24 hours. In the test for interactions between the acetone extract of the seeds and antibiotics, synergistic interactions were observed largely against Gram positive organisms using the FIC indices, (indices of 0.52 - 0.875) with combinations against Gram negatives yielding largely antagonistic interactions (indices of 2.0 to 5.0). Synergy (≥ 1000 times or ≥ 3 Log10 potentiation of the bactericidal activity) against both Gram negative and Gram positive organisms was detected by time kill assays mainly involving the antibiotics tetracycline, chloramphenicol, amoxycillin and penicillin G. Combinations involving erythromycin and ciprofloxacin consistently gave antagonistic or indifferent interactions. We conclude that the acetone extract of Garcinia kola seeds possess strong bactericidal activities against both Gram positive and Gram negative organisms and can be therapeutically useful in the treatment of bacterial infections including the problematic staphylococcal wound infections. In addition, the acetone extract can be a potential source of broad spectrum resistance modifying compounds that can potentially improve the performance of antibiotics in the treatment of drug resistant infections.
- Full Text:
- Authors: Sibanda, Thulani
- Date: 2007
- Subjects: Drug resistance in microorganisms , Garcinia , Antibiotics , Medicinal plants
- Language: English
- Type: Thesis , Masters , MSc (Microbiology)
- Identifier: vital:11242 , http://hdl.handle.net/10353/71 , Drug resistance in microorganisms , Garcinia , Antibiotics , Medicinal plants
- Description: The antibacterial potency of the extracts of the seed of Garcinia kola (bitter kola) was investigated in this study against a panel of referenced, environmental and clinical bacterial strains. The killing rates of the active extract as well as their potential for combination antibacterial therapy with standard antibiotics were also elucidated using standard procedures. The aqueous and acetone extracts of the seed were screened for activity against 27 bacterial isolates. The aqueous extract exhibited activity mainly against Gram positive organisms with Minimum inhibitory concentration (MIC) values ranging from 5 mgml-1 – 20 mgml-1, while the acetone extract showed activity against both Gram negative and Gram positive organisms with MIC values ranging from 10 mgml-1 - 0.156 mgml-1. The acetone extract also showed rapid bactericidal activity against Staphylococcus aureus ATCC 6538 with a 3.097 Log10 reduction in counts within 4 hours at 0.3125 mgml-1 and a 1.582 Log10 reduction against Proteus vulgaris CSIR 0030 at 5 mgml-1 after 1 hour. In addition, the aqueous, methanol and acetone extracts of the seeds also exhibited activity against four clinical strains of Staphylococcus isolated from wound sepsis specimens. The MIC values for the aqueous extract were 10 mgml-1 for all the isolates while the acetone and methanol extracts had lower values ranging from 0.3125 - 0.625 mgml-1. The acetone extract was strongly bactericidal against Staphylococcus aureus OKOH3 resulting in a 2.70 Log10 reduction in counts at 1.25 mgml-1 within 4 hours of exposure and a complete elimination of the organism after 8 hours. The bactericidal vi activity of the same extract against Staphylococcus aureus OKOH1 was weak, achieving only a 2.92 Log10 reduction in counts at 1.25 mgml-1 (4× MIC) in 24 hours. In the test for interactions between the acetone extract of the seeds and antibiotics, synergistic interactions were observed largely against Gram positive organisms using the FIC indices, (indices of 0.52 - 0.875) with combinations against Gram negatives yielding largely antagonistic interactions (indices of 2.0 to 5.0). Synergy (≥ 1000 times or ≥ 3 Log10 potentiation of the bactericidal activity) against both Gram negative and Gram positive organisms was detected by time kill assays mainly involving the antibiotics tetracycline, chloramphenicol, amoxycillin and penicillin G. Combinations involving erythromycin and ciprofloxacin consistently gave antagonistic or indifferent interactions. We conclude that the acetone extract of Garcinia kola seeds possess strong bactericidal activities against both Gram positive and Gram negative organisms and can be therapeutically useful in the treatment of bacterial infections including the problematic staphylococcal wound infections. In addition, the acetone extract can be a potential source of broad spectrum resistance modifying compounds that can potentially improve the performance of antibiotics in the treatment of drug resistant infections.
- Full Text:
Assessment of antibacterial potentials of Garcinia Kola seed extracts and their interactions with antibiotics
- Authors: Sibanda, Thulani
- Date: 2007
- Subjects: Drug resistance in microorganisms , Garcinia , Antibiotics
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10353/19236 , vital:43038
- Description: The antibacterial potency of the extracts of the seed of Garcinia kola (bitter kola) was investigated in this study against a panel of referenced, environmental and clinical bacterial strains. The killing rates of the active extract as well as their potential for combination antibacterial therapy with standard antibiotics were also elucidated using standard procedures. The aqueous and acetone extracts of the seed were screened for activity against 27 bacterial isolates. The aqueous extract exhibited activity mainly against Gram positive organisms with Minimum inhibitory concentration (MIC) values ranging from 5 mgml-1 – 20 mgml-1, while the acetone extract showed activity against both Gram negative and Gram positive organisms with MIC values ranging from 10 mgml-1 - 0.156 mgml-1. The acetone extract also showed rapid bactericidal activity against Staphylococcus aureus ATCC 6538 with a 3.097 Log10 reduction in counts within 4 hours at 0.3125 mgml-1 and a 1.582 Log10 reduction against Proteus vulgaris CSIR 0030 at 5 mgml-1 after 1 hour. In addition, the aqueous, methanol and acetone extracts of the seeds also exhibited activity against four clinical strains of Staphylococcus isolated from wound sepsis specimens. The MIC values for the aqueous extract were 10 mgml-1 for all the isolates while the acetone and methanol extracts had lower values ranging from 0.3125 - 0.625 mgml-1. The acetone extract was strongly bactericidal against Staphylococcus aureus OKOH3 resulting in a 2.70 Log10 reduction in counts at 1.25 mgml-1 within 4 hours of exposure and a complete elimination of the organism after 8 hours. The bactericidal activity of the same extract against Staphylococcus aureus OKOH1 was weak, achieving only a 2.92 Log10 reduction in counts at 1.25 mgml-1 (4× MIC) in 24 hours. In the test for interactions between the acetone extract of the seeds and antibiotics, synergistic interactions were observed largely against Gram positive organisms using the FIC indices, (indices of 0.52 - 0.875) with combinations against Gram negatives yielding largely antagonistic interactions (indices of 2.0 to 5.0). Synergy (≥ 1000 times or ≥ 3 Log10 potentiation of the bactericidal activity) against both Gram negative and Gram positive organisms was detected by time kill assays mainly involving the antibiotics tetracycline, chloramphenicol, amoxycillin and penicillin G. Combinations involving erythromycin and ciprofloxacin consistently gave antagonistic or indifferent interactions. We conclude that the acetone extract of Garcinia kola seeds possess strong bactericidal activities against both Gram positive and Gram negative organisms and can be therapeutically useful in the treatment of bacterial infections including the problematic staphylococcal wound infections. In addition, the acetone extract can be a potential source of broad spectrum resistance modifying compounds that can potentially improve the performance of antibiotics in the treatment of drug resistant infections. , Thesis (MSc)-- Microbiology, University of Fort Hare, 2007
- Full Text:
- Authors: Sibanda, Thulani
- Date: 2007
- Subjects: Drug resistance in microorganisms , Garcinia , Antibiotics
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10353/19236 , vital:43038
- Description: The antibacterial potency of the extracts of the seed of Garcinia kola (bitter kola) was investigated in this study against a panel of referenced, environmental and clinical bacterial strains. The killing rates of the active extract as well as their potential for combination antibacterial therapy with standard antibiotics were also elucidated using standard procedures. The aqueous and acetone extracts of the seed were screened for activity against 27 bacterial isolates. The aqueous extract exhibited activity mainly against Gram positive organisms with Minimum inhibitory concentration (MIC) values ranging from 5 mgml-1 – 20 mgml-1, while the acetone extract showed activity against both Gram negative and Gram positive organisms with MIC values ranging from 10 mgml-1 - 0.156 mgml-1. The acetone extract also showed rapid bactericidal activity against Staphylococcus aureus ATCC 6538 with a 3.097 Log10 reduction in counts within 4 hours at 0.3125 mgml-1 and a 1.582 Log10 reduction against Proteus vulgaris CSIR 0030 at 5 mgml-1 after 1 hour. In addition, the aqueous, methanol and acetone extracts of the seeds also exhibited activity against four clinical strains of Staphylococcus isolated from wound sepsis specimens. The MIC values for the aqueous extract were 10 mgml-1 for all the isolates while the acetone and methanol extracts had lower values ranging from 0.3125 - 0.625 mgml-1. The acetone extract was strongly bactericidal against Staphylococcus aureus OKOH3 resulting in a 2.70 Log10 reduction in counts at 1.25 mgml-1 within 4 hours of exposure and a complete elimination of the organism after 8 hours. The bactericidal activity of the same extract against Staphylococcus aureus OKOH1 was weak, achieving only a 2.92 Log10 reduction in counts at 1.25 mgml-1 (4× MIC) in 24 hours. In the test for interactions between the acetone extract of the seeds and antibiotics, synergistic interactions were observed largely against Gram positive organisms using the FIC indices, (indices of 0.52 - 0.875) with combinations against Gram negatives yielding largely antagonistic interactions (indices of 2.0 to 5.0). Synergy (≥ 1000 times or ≥ 3 Log10 potentiation of the bactericidal activity) against both Gram negative and Gram positive organisms was detected by time kill assays mainly involving the antibiotics tetracycline, chloramphenicol, amoxycillin and penicillin G. Combinations involving erythromycin and ciprofloxacin consistently gave antagonistic or indifferent interactions. We conclude that the acetone extract of Garcinia kola seeds possess strong bactericidal activities against both Gram positive and Gram negative organisms and can be therapeutically useful in the treatment of bacterial infections including the problematic staphylococcal wound infections. In addition, the acetone extract can be a potential source of broad spectrum resistance modifying compounds that can potentially improve the performance of antibiotics in the treatment of drug resistant infections. , Thesis (MSc)-- Microbiology, University of Fort Hare, 2007
- Full Text:
Design and implementation of a network revenue management architecture for marginalised communities
- Authors: Tarwireyi, Paul
- Date: 2007
- Subjects: Community development -- South Africa -- Eastern Cape , Computer network architectures -- South Africa -- Design and construction , Computer network protocols -- South Africa -- Eastern Cape -- Design and construction , Revenue management , Computer networks -- Social aspects
- Language: English
- Type: Thesis , Masters , MSc (Computer Science)
- Identifier: vital:11374 , http://hdl.handle.net/10353/72 , Community development -- South Africa -- Eastern Cape , Computer network architectures -- South Africa -- Design and construction , Computer network protocols -- South Africa -- Eastern Cape -- Design and construction , Revenue management , Computer networks -- Social aspects
- Description: Rural Internet connectivity projects aimed at bridging the digital divide have mushroomed across many developing countries. Most of the projects are deployed as community centred projects. In most of the cases the initial deployment of these projects is funded by governments, multilateral institutions and non-governmental organizations. After the initial deployment, financial sustainability remains one of the greatest challenges facing these projects. In the light of this, externally funded ICT4D interventions should just be used for “bootstrapping” purposes. The communities should be “groomed” to take care of and sustain these projects, eliminating as soon as possible a dependency on external funding. This master thesis presents the design and the implementation of a generic architecture for the management of the costs associated with running a computer network connected to the Internet, The proposed system, called the Network Revenue Management System, enables a network to generate revenue, by charging users for the utilization of network resources. The novelty of the system resides in its flexibility and adaptability, which allow the exploration of both conventional and non-conventional billing options, via the use of suitable ‘adapters’. The final goal of the exploration made possible by this system is the establishment of what is regarded as equitable charging in rural, marginalized communities - such as the community in Dwesa, South Africa.
- Full Text:
- Authors: Tarwireyi, Paul
- Date: 2007
- Subjects: Community development -- South Africa -- Eastern Cape , Computer network architectures -- South Africa -- Design and construction , Computer network protocols -- South Africa -- Eastern Cape -- Design and construction , Revenue management , Computer networks -- Social aspects
- Language: English
- Type: Thesis , Masters , MSc (Computer Science)
- Identifier: vital:11374 , http://hdl.handle.net/10353/72 , Community development -- South Africa -- Eastern Cape , Computer network architectures -- South Africa -- Design and construction , Computer network protocols -- South Africa -- Eastern Cape -- Design and construction , Revenue management , Computer networks -- Social aspects
- Description: Rural Internet connectivity projects aimed at bridging the digital divide have mushroomed across many developing countries. Most of the projects are deployed as community centred projects. In most of the cases the initial deployment of these projects is funded by governments, multilateral institutions and non-governmental organizations. After the initial deployment, financial sustainability remains one of the greatest challenges facing these projects. In the light of this, externally funded ICT4D interventions should just be used for “bootstrapping” purposes. The communities should be “groomed” to take care of and sustain these projects, eliminating as soon as possible a dependency on external funding. This master thesis presents the design and the implementation of a generic architecture for the management of the costs associated with running a computer network connected to the Internet, The proposed system, called the Network Revenue Management System, enables a network to generate revenue, by charging users for the utilization of network resources. The novelty of the system resides in its flexibility and adaptability, which allow the exploration of both conventional and non-conventional billing options, via the use of suitable ‘adapters’. The final goal of the exploration made possible by this system is the establishment of what is regarded as equitable charging in rural, marginalized communities - such as the community in Dwesa, South Africa.
- Full Text:
Development of a web-based interface for a wireless sensor network monitoring system
- Authors: Gumbo, Sibukele
- Date: 2007
- Subjects: Wireless LAN , Sensor networks , Wireless communication systems , Web sites -- Design , User interfaces (Computer systems)
- Language: English
- Type: Thesis , Masters , MSc (Computer Science)
- Identifier: vital:11372 , http://hdl.handle.net/10353/68 , Wireless LAN , Sensor networks , Wireless communication systems , Web sites -- Design , User interfaces (Computer systems)
- Description: In the recent past, wireless sensor technology has undergone advancements in its autonomous data collecting aspects, and has become an area worth investigating in relation to structural monitoring applications. The system described in this thesis aims at acquiring, storing and displaying overhead transmission line related data collected from a wireless sensor network. Open source tools were used in its development and implementation. The inherent linearly aligned topology of transmission line monitoring devices is not without shortcomings; hence analysis of linear node placement, hardware and software components was carried out to determine the feasibility of the system. Their limited data processing capabilities has motivated the development of a post processing wireless sensor application in order to present any collected structural data in an understandable format.
- Full Text:
- Authors: Gumbo, Sibukele
- Date: 2007
- Subjects: Wireless LAN , Sensor networks , Wireless communication systems , Web sites -- Design , User interfaces (Computer systems)
- Language: English
- Type: Thesis , Masters , MSc (Computer Science)
- Identifier: vital:11372 , http://hdl.handle.net/10353/68 , Wireless LAN , Sensor networks , Wireless communication systems , Web sites -- Design , User interfaces (Computer systems)
- Description: In the recent past, wireless sensor technology has undergone advancements in its autonomous data collecting aspects, and has become an area worth investigating in relation to structural monitoring applications. The system described in this thesis aims at acquiring, storing and displaying overhead transmission line related data collected from a wireless sensor network. Open source tools were used in its development and implementation. The inherent linearly aligned topology of transmission line monitoring devices is not without shortcomings; hence analysis of linear node placement, hardware and software components was carried out to determine the feasibility of the system. Their limited data processing capabilities has motivated the development of a post processing wireless sensor application in order to present any collected structural data in an understandable format.
- Full Text:
Enhancing phosphorus availability in some phosphate fixing soils of the Transkei region, South Africa using goat manure
- Authors: Gichangi, Elias Maina
- Date: 2007
- Subjects: Phosphorus in agriculture , Soils -- Phosphorus content , Phosphatic fertilizers , Soils -- Phosphorus content -- South Africa -- Transkei
- Language: English
- Type: Thesis , Doctoral , PhD (Soil Science)
- Identifier: vital:11960 , http://hdl.handle.net/10353/80 , Phosphorus in agriculture , Soils -- Phosphorus content , Phosphatic fertilizers , Soils -- Phosphorus content -- South Africa -- Transkei
- Description: Low availability of soil phosphorus (P) caused by strong sorption of P is a major constraint to agricultural production in most South African soils, particularly those from the high rainfall areas. The aim of this study was therefore to investigate whether combined addition of goat manure with inorganic P fertilizers could enhance P availability in some P fixing soils of the Transkei region, South Africa. The study addressed the following specific objectives (i) to assess P sorption capacities and requirements of selected soils and their relationship with selected soil properties and single point sorption test, (ii) to assess the effects of goat manure and lime addition on P sorption properties of selected P fixing soils (iii) to assess the temporal changes in concentration of inorganic and microbial biomass P fractions following application of inorganic fertilizer P with goat manure in a laboratory incubation experiment, and, (iv) to assess the effects of goat manure application with inorganic phosphate on inorganic and microbial biomass P fractions, P uptake and dry matter yield of maize. Sorption maxima (Smax) of seven soils examined ranged from 192.3 to 909.1 (mg P kg-1) and were highly and positively correlated with sorption affinity constant (r = 0.93, p = 0.01) and organic C (r = 0.71, p = 0.01). The amount of P required for maintaining a soil solution concentration of 0.2 mg P l-1 ranged from 2.1 to 123.5 mg P kg-1 soil. Soils collected from Qweqwe (a Cambisol), Qunu (an Acrisol), Ncihane (a Luvisol) and Bethania (a Ferralsol) had lower external P requirement values and were classified as lower sorbers, whereas soils from Ntlonyana (a Planosol), Chevy Chase (a Ferralsol) and Flagstaff (a Ferralsol) were classified as moderate sorbers. The results suggested that P availability could be compromised in 43 percent iii of the soils studied and that measures to mitigate the adverse effects of P sorption were needed to ensure that P is not a limiting factor to crop production, where such soils are found. Goat manure addition at varying rates (5, 10 and 20 tha-1 dry weight basis) to two of the moderately P fixing soils from Chevy Chase and Flagstaff, reduced P sorption maxima (Smax) compared to the control treatment. Phosphate sorption decreased with increasing amounts of goat manure in both soils but the extent of reduction was greater on Chevy Chase soil than on Flagstaff soil. The relative liming effects of the different rates of goat manure followed the order 20 t GM ha-1 > 10 t GM ha-1 > 5 t GM ha-1. In a separate experiment, addition of inorganic P at varying rates (0, 90, 180, and 360 kg P ha-1) to Flagstaff soil increased labile P fractions (resin P, biomass P and NaHCO3-Pi) and the increases were greater when goat manure was co-applied. The control treatments contained only 17.2 and 27.5 mg P kg-1 of resin extractable P in the un-amended and manure amended treatments, respectively which increased to 118.2 and 122.7 mg P kg-1 on day 28 of incubation. Biomass P concentration was increased from 16.8 to 43.9 mg P kg-1 in P alone treatments but the fraction was greatly enhanced with manure addition, increasing it from 32.6 to 97.7 mg P kg-1. NaOH-Pi was the largest extractable Pi fraction and ranged from 144.3 to 250.6 mg P kg-1 and 107.5 to 213.2 mg P kg-1 in the unamended and manure amended treatments, respectively. Dry matter yield and P uptake by maize grown in the glasshouse were highly and significantly (p = 0.05) correlated with the different P fractions in the soil. The correlations followed the order resin P (r = 0.85) > NaOH-Pi (r = 0.85) > NaHCO3-Pi (r = 0.84) >> biomass P (r = 0.56) for dry matter yield at 6 weeks after planting. At 12 weeks after planting, goat manure had iv highly significant effects on resin P and biomass P but had no effect on NaHCO3-Pi and NaOH–Pi. The combination of biomass P, resin P and NaHCO3-Pi explained 75.8 percent of the variation in dry matter yield of which 63.0 percent of the variation was explained by biomass P alone. The greatest increase in biomass P occurred when added P was co-applied with 5 or 10 tha-1 goat manure. The predictive equation for maize dry matter yield (DM) was: DM (g) = 1.897 biomass P + 0.645 resin P (r = 0.73). Resin P was the fraction that was most depleted due to plant uptake and decreased by 56 to 68 percent between the 6th week and the 12th week of sampling indicating that it played a greater role in supplying plant available P. The results therefore suggested that the use of goat manure may allow resource poor farmers to use lower levels of commercial phosphate fertilizers because of its effect to reduce soil P sorption. In addition, higher increases in biomass P due to manure addition observed at lower rates of added P indicated that goat manure has potential for enhancing bioavailability and fertilizer use efficiency of small inorganic P applications.
- Full Text:
- Authors: Gichangi, Elias Maina
- Date: 2007
- Subjects: Phosphorus in agriculture , Soils -- Phosphorus content , Phosphatic fertilizers , Soils -- Phosphorus content -- South Africa -- Transkei
- Language: English
- Type: Thesis , Doctoral , PhD (Soil Science)
- Identifier: vital:11960 , http://hdl.handle.net/10353/80 , Phosphorus in agriculture , Soils -- Phosphorus content , Phosphatic fertilizers , Soils -- Phosphorus content -- South Africa -- Transkei
- Description: Low availability of soil phosphorus (P) caused by strong sorption of P is a major constraint to agricultural production in most South African soils, particularly those from the high rainfall areas. The aim of this study was therefore to investigate whether combined addition of goat manure with inorganic P fertilizers could enhance P availability in some P fixing soils of the Transkei region, South Africa. The study addressed the following specific objectives (i) to assess P sorption capacities and requirements of selected soils and their relationship with selected soil properties and single point sorption test, (ii) to assess the effects of goat manure and lime addition on P sorption properties of selected P fixing soils (iii) to assess the temporal changes in concentration of inorganic and microbial biomass P fractions following application of inorganic fertilizer P with goat manure in a laboratory incubation experiment, and, (iv) to assess the effects of goat manure application with inorganic phosphate on inorganic and microbial biomass P fractions, P uptake and dry matter yield of maize. Sorption maxima (Smax) of seven soils examined ranged from 192.3 to 909.1 (mg P kg-1) and were highly and positively correlated with sorption affinity constant (r = 0.93, p = 0.01) and organic C (r = 0.71, p = 0.01). The amount of P required for maintaining a soil solution concentration of 0.2 mg P l-1 ranged from 2.1 to 123.5 mg P kg-1 soil. Soils collected from Qweqwe (a Cambisol), Qunu (an Acrisol), Ncihane (a Luvisol) and Bethania (a Ferralsol) had lower external P requirement values and were classified as lower sorbers, whereas soils from Ntlonyana (a Planosol), Chevy Chase (a Ferralsol) and Flagstaff (a Ferralsol) were classified as moderate sorbers. The results suggested that P availability could be compromised in 43 percent iii of the soils studied and that measures to mitigate the adverse effects of P sorption were needed to ensure that P is not a limiting factor to crop production, where such soils are found. Goat manure addition at varying rates (5, 10 and 20 tha-1 dry weight basis) to two of the moderately P fixing soils from Chevy Chase and Flagstaff, reduced P sorption maxima (Smax) compared to the control treatment. Phosphate sorption decreased with increasing amounts of goat manure in both soils but the extent of reduction was greater on Chevy Chase soil than on Flagstaff soil. The relative liming effects of the different rates of goat manure followed the order 20 t GM ha-1 > 10 t GM ha-1 > 5 t GM ha-1. In a separate experiment, addition of inorganic P at varying rates (0, 90, 180, and 360 kg P ha-1) to Flagstaff soil increased labile P fractions (resin P, biomass P and NaHCO3-Pi) and the increases were greater when goat manure was co-applied. The control treatments contained only 17.2 and 27.5 mg P kg-1 of resin extractable P in the un-amended and manure amended treatments, respectively which increased to 118.2 and 122.7 mg P kg-1 on day 28 of incubation. Biomass P concentration was increased from 16.8 to 43.9 mg P kg-1 in P alone treatments but the fraction was greatly enhanced with manure addition, increasing it from 32.6 to 97.7 mg P kg-1. NaOH-Pi was the largest extractable Pi fraction and ranged from 144.3 to 250.6 mg P kg-1 and 107.5 to 213.2 mg P kg-1 in the unamended and manure amended treatments, respectively. Dry matter yield and P uptake by maize grown in the glasshouse were highly and significantly (p = 0.05) correlated with the different P fractions in the soil. The correlations followed the order resin P (r = 0.85) > NaOH-Pi (r = 0.85) > NaHCO3-Pi (r = 0.84) >> biomass P (r = 0.56) for dry matter yield at 6 weeks after planting. At 12 weeks after planting, goat manure had iv highly significant effects on resin P and biomass P but had no effect on NaHCO3-Pi and NaOH–Pi. The combination of biomass P, resin P and NaHCO3-Pi explained 75.8 percent of the variation in dry matter yield of which 63.0 percent of the variation was explained by biomass P alone. The greatest increase in biomass P occurred when added P was co-applied with 5 or 10 tha-1 goat manure. The predictive equation for maize dry matter yield (DM) was: DM (g) = 1.897 biomass P + 0.645 resin P (r = 0.73). Resin P was the fraction that was most depleted due to plant uptake and decreased by 56 to 68 percent between the 6th week and the 12th week of sampling indicating that it played a greater role in supplying plant available P. The results therefore suggested that the use of goat manure may allow resource poor farmers to use lower levels of commercial phosphate fertilizers because of its effect to reduce soil P sorption. In addition, higher increases in biomass P due to manure addition observed at lower rates of added P indicated that goat manure has potential for enhancing bioavailability and fertilizer use efficiency of small inorganic P applications.
- Full Text:
Growth performance, carcass characteristics and meat quality of Nguni, Bonsmara and Angus steers raised on natural pasture
- Authors: Muchenje, Voster
- Date: 2007
- Subjects: Cattle -- Feeding and feeds , Cattle -- Growth , Nguni cattle , Aberdeen -- Angus cattle , Bonsmara cattle , Meat industry and trade -- Quality control
- Language: English
- Type: Thesis , Doctoral , PhD (Animal Science)
- Identifier: vital:11580 , http://hdl.handle.net/10353/199 , Cattle -- Feeding and feeds , Cattle -- Growth , Nguni cattle , Aberdeen -- Angus cattle , Bonsmara cattle , Meat industry and trade -- Quality control
- Description: The objective of the current study was to compare tick loads, growth, carcass characteristics and meat quality of Nguni, Bonsmara and Angus steers raised on natural pasture. A total of 30, 7-month old steers each of Bonsmara and Angus, and 40 Nguni steers were kept at the University of Fort Hare Farm till slaughter at 18 months. Monthly weights of the steers were recorded. Carcasses were electrically stimulated. The m. longissimus thoracis et lumborum was sampled for the measurement of meat colour, pH, drip loss, sarcomere length (SL), water holding capacity (WHC), cooking losses, myofibrillar fragmentation length (MFL), Warner Bratzler shear force (WBSF), fatty acid profiles and sensory characteristics of the steers. Urine samples were collected at the slaughter line for the determination of stress hormone concentrations. The Nguni had the lowest tick load (P < 0.05) while the Angus had the highest tick load (P < 0.05). Tick load did not affect the growth rate and carcass characteristics of the steers. Bonsmara and Angus steers had higher (P < 0.05) carcass weight and dressing percentage than the Nguni steers. Meat quality characteristics were similar (P > 0.05) among all the breeds, except that Nguni meat was darker (L*) (P < 0.05) than meat from the other two breeds. The Bonsmara had the highest (P > 0.05) concentrations while the Nguni had the lowest (P > 0.05) concentrations of stress hormones. There were significant (P < 0.05) correlations between WB values of meat aged for two and 21 days in Nguni and Bonsmara, but not in Angus. The correlations among stress responsiveness hormones and meat quality were breed-dependent. Except monounsaturated fatty acids (MUFA) and the n-6/n-3 ratio, fatty acid profiles among the breeds were similar (P > 0.05). Cholesterol levels among the breeds were similar (P > 0.05). The Nguni had the best (P < 0.05) sensory characteristics, such as flavour and tenderness. It can be concluded that while the Nguni is a small framed breed, its meat quality is similar to that of Bonsmara and Angus and has the best meat taste when raised on natural pasture.
- Full Text:
- Authors: Muchenje, Voster
- Date: 2007
- Subjects: Cattle -- Feeding and feeds , Cattle -- Growth , Nguni cattle , Aberdeen -- Angus cattle , Bonsmara cattle , Meat industry and trade -- Quality control
- Language: English
- Type: Thesis , Doctoral , PhD (Animal Science)
- Identifier: vital:11580 , http://hdl.handle.net/10353/199 , Cattle -- Feeding and feeds , Cattle -- Growth , Nguni cattle , Aberdeen -- Angus cattle , Bonsmara cattle , Meat industry and trade -- Quality control
- Description: The objective of the current study was to compare tick loads, growth, carcass characteristics and meat quality of Nguni, Bonsmara and Angus steers raised on natural pasture. A total of 30, 7-month old steers each of Bonsmara and Angus, and 40 Nguni steers were kept at the University of Fort Hare Farm till slaughter at 18 months. Monthly weights of the steers were recorded. Carcasses were electrically stimulated. The m. longissimus thoracis et lumborum was sampled for the measurement of meat colour, pH, drip loss, sarcomere length (SL), water holding capacity (WHC), cooking losses, myofibrillar fragmentation length (MFL), Warner Bratzler shear force (WBSF), fatty acid profiles and sensory characteristics of the steers. Urine samples were collected at the slaughter line for the determination of stress hormone concentrations. The Nguni had the lowest tick load (P < 0.05) while the Angus had the highest tick load (P < 0.05). Tick load did not affect the growth rate and carcass characteristics of the steers. Bonsmara and Angus steers had higher (P < 0.05) carcass weight and dressing percentage than the Nguni steers. Meat quality characteristics were similar (P > 0.05) among all the breeds, except that Nguni meat was darker (L*) (P < 0.05) than meat from the other two breeds. The Bonsmara had the highest (P > 0.05) concentrations while the Nguni had the lowest (P > 0.05) concentrations of stress hormones. There were significant (P < 0.05) correlations between WB values of meat aged for two and 21 days in Nguni and Bonsmara, but not in Angus. The correlations among stress responsiveness hormones and meat quality were breed-dependent. Except monounsaturated fatty acids (MUFA) and the n-6/n-3 ratio, fatty acid profiles among the breeds were similar (P > 0.05). Cholesterol levels among the breeds were similar (P > 0.05). The Nguni had the best (P < 0.05) sensory characteristics, such as flavour and tenderness. It can be concluded that while the Nguni is a small framed breed, its meat quality is similar to that of Bonsmara and Angus and has the best meat taste when raised on natural pasture.
- Full Text:
Narratives of South African heteroseual relationships: understanding masculine and feminine togetherness
- Authors: Tracey, Tiffany
- Date: 2007
- Subjects: Heterosexuality , Heterosexism , Homosexuality , Gender identity
- Language: English
- Type: Thesis , Doctoral , D Soc Sc (Psych)
- Identifier: vital:11601 , http://hdl.handle.net/10353/176 , Heterosexuality , Heterosexism , Homosexuality , Gender identity
- Description: Heterosexuality often appears as a monolithic way of being that has been disciplinarily defined as right and natural for all sexual subjects (Foucault, 1979). However, it may also be viewed as a social construction, subject to alteration and variation according to social and historical context. In the following research, the stories of ten couples and from the South African soap opera Isidingo reveal the ways that heteronorms shape togetherness between men and women. In the research a queer stance is used to interrogate the ways that togetherness appears as natural and normal, such that the contingency of such togetherness is revealed. The queer stance was used to unsettle the unquestioned assumption of heteronormativity by interrogating the construction from a political position not included by the norm (Stein & Plummer, 1994). Within the general queer stance the concept of performance has been used to account for the ways in which subjects are able to unsettle normative constraints: Butler’s (1993) conception of repetition, Holzman’s (1991) account of the revolutionary developmental potential of performance, Billig’s (1991) understanding of the rhetorical constructions of everyday philosophers. Further Bakhtin’s (1994) dialogic ontology suggests that utterances, performances and/or narratives Using these theoretical underpinnings, the narratives show how stories of togetherness collude with heteronorms while at the same time existing alongside alternative forms of togetherness. Possibly because norms are broad, overarching constructions, they do not define the entirety of the couples’ tales. Rather moments of resistance and alteration are interwoven with normative themes. This unpredictable ambivalence appears in the couples narratives as the assertion that all relationships are the same, and that all relationships are unique. Couples position themselves within a social network, and this network instructs the couple on heteronormative ways of being together. They also witness normative performances in a way that is similar to the observation of disciplines, suggested by Foucault (1979). Although couples often go with their social network’s observations, the manner in which couples position themselves within this network assists them in arguing for alternatives to heteronorms. Spatial expressions also at times serve to fix togetherness. Homes are structured in line with social constructions of heteronorms. However, couples can and do mould their understandings of their homes, such space is reveal as an intersection between social and individual concerns. Narratives of work again reveal that heteronorms structure but can also be ignored within heterosexual relationships. Couples tell of receiving particular benefits from normative performances, and it is likely that these dividends make it difficult to opt for an altered version of togetherness. At the same time, the gender dualism of a heteronormative division of labour inserts oppression into togetherness, and this may lead couples to seek an unusual way of being together. In these ways, heterosexuality can be read as a multiple and contingent performance, rather than an immovable, unchangeable imperative.
- Full Text:
- Authors: Tracey, Tiffany
- Date: 2007
- Subjects: Heterosexuality , Heterosexism , Homosexuality , Gender identity
- Language: English
- Type: Thesis , Doctoral , D Soc Sc (Psych)
- Identifier: vital:11601 , http://hdl.handle.net/10353/176 , Heterosexuality , Heterosexism , Homosexuality , Gender identity
- Description: Heterosexuality often appears as a monolithic way of being that has been disciplinarily defined as right and natural for all sexual subjects (Foucault, 1979). However, it may also be viewed as a social construction, subject to alteration and variation according to social and historical context. In the following research, the stories of ten couples and from the South African soap opera Isidingo reveal the ways that heteronorms shape togetherness between men and women. In the research a queer stance is used to interrogate the ways that togetherness appears as natural and normal, such that the contingency of such togetherness is revealed. The queer stance was used to unsettle the unquestioned assumption of heteronormativity by interrogating the construction from a political position not included by the norm (Stein & Plummer, 1994). Within the general queer stance the concept of performance has been used to account for the ways in which subjects are able to unsettle normative constraints: Butler’s (1993) conception of repetition, Holzman’s (1991) account of the revolutionary developmental potential of performance, Billig’s (1991) understanding of the rhetorical constructions of everyday philosophers. Further Bakhtin’s (1994) dialogic ontology suggests that utterances, performances and/or narratives Using these theoretical underpinnings, the narratives show how stories of togetherness collude with heteronorms while at the same time existing alongside alternative forms of togetherness. Possibly because norms are broad, overarching constructions, they do not define the entirety of the couples’ tales. Rather moments of resistance and alteration are interwoven with normative themes. This unpredictable ambivalence appears in the couples narratives as the assertion that all relationships are the same, and that all relationships are unique. Couples position themselves within a social network, and this network instructs the couple on heteronormative ways of being together. They also witness normative performances in a way that is similar to the observation of disciplines, suggested by Foucault (1979). Although couples often go with their social network’s observations, the manner in which couples position themselves within this network assists them in arguing for alternatives to heteronorms. Spatial expressions also at times serve to fix togetherness. Homes are structured in line with social constructions of heteronorms. However, couples can and do mould their understandings of their homes, such space is reveal as an intersection between social and individual concerns. Narratives of work again reveal that heteronorms structure but can also be ignored within heterosexual relationships. Couples tell of receiving particular benefits from normative performances, and it is likely that these dividends make it difficult to opt for an altered version of togetherness. At the same time, the gender dualism of a heteronormative division of labour inserts oppression into togetherness, and this may lead couples to seek an unusual way of being together. In these ways, heterosexuality can be read as a multiple and contingent performance, rather than an immovable, unchangeable imperative.
- Full Text:
Rural internet connectivity: a development in Dwesa-Cwebe, Eastern Cape, South Africa
- Authors: Mandioma, Martin
- Date: 2007
- Subjects: Internet -- South Africa -- Eastern Cape
- Language: English
- Type: Thesis , Masters , MSc (Computer Science)
- Identifier: vital:11376 , http://hdl.handle.net/10353/78 , Internet -- South Africa -- Eastern Cape
- Description: This thesis presents aspects of Internet connectivity in rural South Africa. The work looks at government initiatives being undertaken to connect rural communities to up-to-date information networks. Various projects that seek to connect rural areas of South Africa, as well as other remote areas around the world, are discussed. These projects present many novel ideas that have been successfully used to link rural communities in remote areas with the information age. In particular, wired and wireless access technologies that can be implemented to connect remote communities to the Internet are discussed. A field test utilizing GPRS, VSAT and WiMAX was implemented in Dwesa-Cwebe, Eastern Cape Province, South Africa. VSAT proved to offer better Internet connectivity in terms of throughput and latency. WiMAX was then successfully implemented to relay the signal over the remote area of Dwesa-Cwebe, thus effectively providing Internet connectivity to an area with limited cell phone coverage and no telephone lines.
- Full Text:
- Authors: Mandioma, Martin
- Date: 2007
- Subjects: Internet -- South Africa -- Eastern Cape
- Language: English
- Type: Thesis , Masters , MSc (Computer Science)
- Identifier: vital:11376 , http://hdl.handle.net/10353/78 , Internet -- South Africa -- Eastern Cape
- Description: This thesis presents aspects of Internet connectivity in rural South Africa. The work looks at government initiatives being undertaken to connect rural communities to up-to-date information networks. Various projects that seek to connect rural areas of South Africa, as well as other remote areas around the world, are discussed. These projects present many novel ideas that have been successfully used to link rural communities in remote areas with the information age. In particular, wired and wireless access technologies that can be implemented to connect remote communities to the Internet are discussed. A field test utilizing GPRS, VSAT and WiMAX was implemented in Dwesa-Cwebe, Eastern Cape Province, South Africa. VSAT proved to offer better Internet connectivity in terms of throughput and latency. WiMAX was then successfully implemented to relay the signal over the remote area of Dwesa-Cwebe, thus effectively providing Internet connectivity to an area with limited cell phone coverage and no telephone lines.
- Full Text:
The classification of some fuzzy subgroups of finite groups under a natural equivalence and its extension, with particular emphasis on the number of equivalence classes
- Authors: Ndiweni, Odilo
- Date: 2007
- Subjects: Fuzzy sets , Maximal functions , Finite groups , Equivalence classes (Set theory)
- Language: English
- Type: Thesis , Masters , M Sc (Mathematics)
- Identifier: vital:11587 , http://hdl.handle.net/10353/88 , Fuzzy sets , Maximal functions , Finite groups , Equivalence classes (Set theory)
- Description: In this thesis we use the natural equivalence of fuzzy subgroups studied by Murali and Makamba [25] to characterize fuzzy subgroups of some finite groups. We focus on the determination of the number of equivalence classes of fuzzy subgroups of some selected finite groups using this equivalence relation and its extension. Firstly we give a brief discussion on the theory of fuzzy sets and fuzzy subgroups. We prove a few properties of fuzzy sets and fuzzy subgroups. We then introduce the selected groups namely the symmetric group 3 S , dihedral group 4 D , the quaternion group Q8 , cyclic p-group pn G = Z/ , pn qm G = Z/ + Z/ , p q r G Z Z Z n m = / + / + / and pn qm r s G = Z/ + Z/ + Z/ where p,q and r are distinct primes and n,m, s Î N/ . We also present their subgroups structures and construct lattice diagrams of subgroups in order to study their maximal chains. We compute the number of maximal chains and give a brief explanation on how the maximal chains are used in the determination of the number of equivalence classes of fuzzy subgroups. In determining the number of equivalence classes of fuzzy subgroups of a group, we first list down all the maximal chains of the group. Secondly we pick any maximal chain and compute the number of distinct fuzzy subgroups represented by that maximal chain, expressing each fuzzy subgroup in the form of a keychain. Thereafter we pick the next maximal chain and count the number of equivalence classes of fuzzy subgroups not counted in the first chain. We proceed inductively until all the maximal chains have been exhausted. The total number of fuzzy subgroups obtained in all the maximal chains represents the number of equivalence classes of fuzzy subgroups for the entire group, (see sections 3.2.1, 3.2.2, 3.2.6, 3.2.8, 3.2.9, 3.2.15, 3.16 and 3.17 for the case of selected finite groups). We study, establish and prove the formulae for the number of maximal chains for the groups pn qm G = Z/ + Z/ , p q r G Z Z Z n m = / + / + / and pn qm r s G = Z/ + Z/ + Z/ where p,q and r are distinct primes and n,m, s Î N/ . To accomplish this, we use lattice diagrams of subgroups of these groups to identify the maximal chains. For instance, the group pn qm G = Z/ + Z/ would require the use of a 2- dimensional rectangular diagram (see section 3.2.18 and 5.3.5), while for the group pn qm r s G = Z/ + Z/ + Z/ we execute 3- dimensional lattice diagrams of subgroups (see section 5.4.2, 5.4.3, 5.4.4, 5.4.5 and 5.4.6). It is through these lattice diagrams that we identify routes through which to carry out the extensions. Since fuzzy subgroups represented by maximal chains are viewed as keychains, we give a brief discussion on the notion of keychains, pins and their extensions. We present propositions and proofs on why this counting technique is justifiable. We derive and prove formulae for the number of equivalence classes of the groups pn qm G = Z/ + Z/ , p q r G Z Z Z n m = / + / + / and pn qm r s G = Z/ + Z/ + Z/ where p,q and r are distinct primes and n,m, s Î N/ . We give a detailed explanation and illustrations on how this keychain extension principle works in Chapter Five. We conclude by giving specific illustrations on how we compute the number of equivalence classes of a fuzzy subgroup for the group p2 q2 r 2 G = Z/ + Z/ + Z/ from the number of fuzzy subgroups of the group p q r G = Z/ + Z/ + Z/ 1 2 2 . This illustrates a general technique of computing the number of fuzzy subgroups of G = Z/ + Z/ + Z/ from the number of fuzzy subgroups of 1 -1 = / + / + / pn qm r s G Z Z Z . Our illustration also shows two ways of extending from a lattice diagram of 1 G to that of G .
- Full Text:
- Authors: Ndiweni, Odilo
- Date: 2007
- Subjects: Fuzzy sets , Maximal functions , Finite groups , Equivalence classes (Set theory)
- Language: English
- Type: Thesis , Masters , M Sc (Mathematics)
- Identifier: vital:11587 , http://hdl.handle.net/10353/88 , Fuzzy sets , Maximal functions , Finite groups , Equivalence classes (Set theory)
- Description: In this thesis we use the natural equivalence of fuzzy subgroups studied by Murali and Makamba [25] to characterize fuzzy subgroups of some finite groups. We focus on the determination of the number of equivalence classes of fuzzy subgroups of some selected finite groups using this equivalence relation and its extension. Firstly we give a brief discussion on the theory of fuzzy sets and fuzzy subgroups. We prove a few properties of fuzzy sets and fuzzy subgroups. We then introduce the selected groups namely the symmetric group 3 S , dihedral group 4 D , the quaternion group Q8 , cyclic p-group pn G = Z/ , pn qm G = Z/ + Z/ , p q r G Z Z Z n m = / + / + / and pn qm r s G = Z/ + Z/ + Z/ where p,q and r are distinct primes and n,m, s Î N/ . We also present their subgroups structures and construct lattice diagrams of subgroups in order to study their maximal chains. We compute the number of maximal chains and give a brief explanation on how the maximal chains are used in the determination of the number of equivalence classes of fuzzy subgroups. In determining the number of equivalence classes of fuzzy subgroups of a group, we first list down all the maximal chains of the group. Secondly we pick any maximal chain and compute the number of distinct fuzzy subgroups represented by that maximal chain, expressing each fuzzy subgroup in the form of a keychain. Thereafter we pick the next maximal chain and count the number of equivalence classes of fuzzy subgroups not counted in the first chain. We proceed inductively until all the maximal chains have been exhausted. The total number of fuzzy subgroups obtained in all the maximal chains represents the number of equivalence classes of fuzzy subgroups for the entire group, (see sections 3.2.1, 3.2.2, 3.2.6, 3.2.8, 3.2.9, 3.2.15, 3.16 and 3.17 for the case of selected finite groups). We study, establish and prove the formulae for the number of maximal chains for the groups pn qm G = Z/ + Z/ , p q r G Z Z Z n m = / + / + / and pn qm r s G = Z/ + Z/ + Z/ where p,q and r are distinct primes and n,m, s Î N/ . To accomplish this, we use lattice diagrams of subgroups of these groups to identify the maximal chains. For instance, the group pn qm G = Z/ + Z/ would require the use of a 2- dimensional rectangular diagram (see section 3.2.18 and 5.3.5), while for the group pn qm r s G = Z/ + Z/ + Z/ we execute 3- dimensional lattice diagrams of subgroups (see section 5.4.2, 5.4.3, 5.4.4, 5.4.5 and 5.4.6). It is through these lattice diagrams that we identify routes through which to carry out the extensions. Since fuzzy subgroups represented by maximal chains are viewed as keychains, we give a brief discussion on the notion of keychains, pins and their extensions. We present propositions and proofs on why this counting technique is justifiable. We derive and prove formulae for the number of equivalence classes of the groups pn qm G = Z/ + Z/ , p q r G Z Z Z n m = / + / + / and pn qm r s G = Z/ + Z/ + Z/ where p,q and r are distinct primes and n,m, s Î N/ . We give a detailed explanation and illustrations on how this keychain extension principle works in Chapter Five. We conclude by giving specific illustrations on how we compute the number of equivalence classes of a fuzzy subgroup for the group p2 q2 r 2 G = Z/ + Z/ + Z/ from the number of fuzzy subgroups of the group p q r G = Z/ + Z/ + Z/ 1 2 2 . This illustrates a general technique of computing the number of fuzzy subgroups of G = Z/ + Z/ + Z/ from the number of fuzzy subgroups of 1 -1 = / + / + / pn qm r s G Z Z Z . Our illustration also shows two ways of extending from a lattice diagram of 1 G to that of G .
- Full Text:
- «
- ‹
- 1
- ›
- »